Yes it will save bandwidth data even during a reboot, as the router still goes through the shutdown process. It does not how ever save data during any sort of power outage where the router is unable to go through the shut down process.

What NeutralGold says is 100% accurate. I save my bandwidth stats to a CIFS/SMB share and rebooting the router (shutdown, etc.) via GUI or CLI does the right thing (meaning bandwidth stats *are* written to the CIFS/SMB file immediately prior to reboot). You can verify yourself -- look at the file modification time of the CIFS/SMB file before and after a reboot.

But on power loss or equivalent, you lose the statistics between the last time data was saved to the CIFS/SMB share and the time power was lost. It should be obvious why: the data is only written to the CIFS/SMB share at an interval of what you choose, and the lowest (most granular) frequency is 1 hour.

yes, I did notice the modification time on my stat file before posting here. I guess the rstat file counts towards the daily/weeky/monthly usage only as a reboot wipes out the stats e.g. in "Last 24 hours" doesn't it? Is this Last 24 hours data saved somewhere else?

I am under the impression that the exact same statistics file is used for the "Last 24 hours" feature. Thus, when you reboot your router, and the file modification time is changed (because all bandwidth data is being flushed/written to that file), you lose nothing.